A Miami judge gave final approval Monday to a $410 million Bank of America settlement related to a class-action lawsuit that accused it of charging excessive overdraft fees to millions of debit-card customers.

U.S. District Judge James Lawrence King approved the settlement, which will give account holders as much as 45 cents on the dollar on their claims, said Miami attorney Aaron Podhurst of Podhurst Orseck, co-lead counsel for the plaintiffs.

Customers will automatically receive the payment; no paperwork is necessary, he said.

The judge also approved $123 million in attorneys fees — or 30 percent of the settlement, following an all-day hearing in Miami that included objections to the settlement and the fees.

“We’re very pleased that the court agreed with us and thought the settlement was fair and adequate and reasonable, and that he recognized the hard work that the lawyers had done,” Podhurst said in a telephone interview after the ruling. The fees will be apportioned among about 40 law firms and hundreds of lawyers, and no breakdown has yet been determined, he said.

Lawsuits from around the country, which claimed banks charged excessive fees when debit-card users made purchases that exceeded their balances, were consolidated in 2009 in Miami.

Bank of America was the first to settle among about 35 U.S. banks named in the class-action litigation. Other major banks include JPMorgan Chase, Citigroup, Wells Fargo and San Francisco-based Union Bank, which recently agreed to a $35 million settlement. That accord has yet to be approved in court, Podhurst said.

The Bank of America settlement benefits the bank’s customers who used their debit cards since 2001 and were charged overdraft fees as a result of “debit re-sequencing” — or the order in which postings were processed. The lawsuit charged that banks waited to process charges until days after a purchase was made, when users’ accounts were depleted; or manipulated charges so that large purchases that would deplete an account would be processed first, triggering overdraft fees on smaller purchases made earlier.

Because some debit card users from the early years cannot be identified, the court set aside about 12.5 percent of the settlement for educational institutions that teach consumers about financial and banking practices, Podhurst said.

“This a marvelous result for the members of the class,” King said at the hearing, Bloomberg News reported.